A novel functional form for approximating the conditional scalars in turbulent reacting flows is introduced based on the Bernstein polynomial. Multi-scalar measurement data of turbulent premixed and non-premixed flames are used to demonstrate that the new functional form provides an excellent reduced-order model for the conditional scalars. This model order reduction technique can be used to improve the accuracy, reduce the computational cost and enhance the spatial localization of the Conditional Source-term Estimation (CSE) model. CSE is a turbulence-chemistry interaction model similar to the Conditional Moment Closure (CMC) model, except that the conditional scalars are estimated from the filtered field in an ensemble of LES cells using an integral equation. An a priori analysis using the DNS data of a series of statistically planar turbulent premixed flames shows that using Bernstein polynomials as the presumed functional form for the conditional scalars provides better regularization than the conventional CSE approach. Furthermore, the ensemble size – that was previously kept on the order of thousands of LES cells in the singly-conditioned CSE – can be reduced to as low as 16 LES cells. This enhanced localization approach reduces the modelling error and the computational cost compared to the conventional CSE approach for tabulated and reduced chemistry models.

基于伯恩斯坦多项式引入了一种新的函数形式，用于逼近湍流反应流中的条件标量。湍流预混和非预混火焰的多标量测量数据被用来证明新的函数形式为条件标量提供了一个很好的降阶模型。该模型降阶技术可用于提高精度、降低计算成本并增强条件源项估计（CSE）模型的空间定位。CSE 是类似于条件矩闭合 (CMC) 模型的湍流-化学相互作用模型，不同之处在于条件标量是使用积分方程从 LES 单元集合中的​​过滤场估计的。一个先验使用一系列统计平面湍流预混火焰的 DNS 数据进行的分析表明，使用 Bernstein 多项式作为条件标量的假定函数形式提供了比传统 CSE 方法更好的正则化。此外，集合大小——之前在单条件 CSE 中保持在数千个 LES 细胞的数量级——可以减少到低至 16 个 LES 细胞。与用于列表和简化化学模型的传统 CSE 方法相比，这种增强的定位方法减少了建模错误和计算成本。